Editing Brownian tree (section)

=== Limit of Galton-Watson trees ===
Consider a [[Galton-Watson tree]] whose reproduction law has finite non-zero variance, conditioned to have <math>n</math> nodes. Let <math>\tfrac{1}{\sqrt{n}}G_n</math> be this tree, with the edge lengths divided by <math>\sqrt{n}</math>. In other words, each edge has length <math>\tfrac{1}{\sqrt{n}}</math>. The construction can be formalized by considering the Galton-Watson tree as a metric space or by using renormalized [[Galton-Watson tree|contour processes]].
{{Math theorem
| math_statement = <math>\frac{1}{\sqrt{n}}G_n</math> converges in distribution to a random real tree, which we call a '''Brownian tree'''.
| name = Definition and Theorem
}}

Here, the limit used is the [[convergence in distribution]] of [[stochastic process]]es in the [[Skorokhod space]] (if we consider the contour processes) or the convergence in distribution defined from the [[Hausdorff distance]] (if we consider the metric spaces).